Question

NO LINKS!! URGENT HELP PLEASE!!

25. Use the relationship in the diagrams below to solve for the given variable.
Justify your solution with a definition or theorem.​

Answer 1

x = 110°

Explanation:

The opposite angles are equal in a parallelogram

3x - 60 = 2x + 50

⇒ 3x - 2x = 60 + 50

⇒ x = 110°

Answer 2

x = 110°

Explanation:

As the top and bottom line segments of the given shape are the same length and parallel (indicated by the tick marks and arrows), the shape is a parallelogram.

As the opposite angles of a parallelogram are equal, to find the value of the variable x, equate the two angle expressions and solve for x:

`\begin{aligned}3x-60^(\circ)&=2x+50^(\circ)\\3x-60^(\circ)-2x&=2x+50^(\circ)-2x\\x-60^(\circ)&=50^(\circ)\\x-60^(\circ)+60^(\circ)&=50^(\circ)+60^(\circ)\\x&=110^(\circ)\end{aligned}`

Therefore, the value of x is 110°.

Note: There must be an error in the question. If x = 110°, each angle measures 270°, which is impossible since the sum of the interior angles of a quadrilateral is 360°.